Long bone loading histories are commonly evaluated using a beam model by calculating cross-sectional second moments of areas (SMAs). Without in vivo strain data, SMA analyses commonly make two explicit or implicit assumptions. First, while it has long been known that axial compression superimposed on bending shifts neutral axes away from cross-sectional area centroids, most analyses assume that cross-sectional properties calculated through the area centroid approximate cross-sectional strength. Second, the orientation of maximum bending rigidity is often assumed to reflect the orientation of peak or habitual bending forces the bone experiences. These assumptions are tested in sheep in which rosette strain gauges mounted at three locations around the tibia and metatarsal midshafts measured in vivo strains during treadmill running at 1.5 m/sec. Calculated normal strain distributions confirm that the neutral axis of bending does not run through the midshaft centroid. In these animals, orientations of the principal centroidal axes around which maximum SMAs (Imax) are calculated are not in the same planes in which the bones experienced bending. Cross-sectional properties calculated using centroidal axes have substantial differences in magnitude (up to 55%) but high correlations in pattern compared to cross-sectional properties calculated around experimentally determined neutral axes. Thus interindividual comparisons of cross-sectional properties calculated from centroidal axes may be useful in terms of pattern, but are subject to high errors in terms of absolute values. In addition, cross-sectional properties do not necessarily provide reliable data on the orientations of loads to which bones are subjected.

In most mammals, especially those adapted for cursoriality, distal limb bones are thinner than more proximal bones, giving the limb skeleton a tapered shape (Smith and Savage, 1956;Alexander, 1980Alexander, , 1996Hildebrand, 1985;Lieberman and Pearson, 2001;Currey, 2002). In sheep, for example, midshaft cortical areas decrease about 16% between the femur and tibia, and 24% between the tibia and metatarsal. Limb tapering is generally thought to save energy by reducing a limb's moment of inertia (Hildebrand, 1985). How much energy is saved by distal tapering has been the subject of debate, but is probably considerable in most species. While Taylor et al. (1974) found that three species (cheetah, gazelle and goats) with different limb configurations had similar energy costs (VO∑·g -1 ·h -1 ) over a range of speeds, the conclusions of the study may be flawed because the animals were not run at comparable speeds. The results of Taylor et al. (1974) contradict not only theoretical predictions (for example, see Hildebrand, 1985), but also more controlled studies such as by Myers and Steudel (1985), who found that redistributing 3.6·kg from the thigh to the ankles in trained humans increases the metabolic cost of running at 2.68·m·s -1 by 15%.Limb tapering may save energy during swing, but may also affect bone strength during stance. Limbs during stance are usually modeled as cylinders subject to a combination of bending and axial compression from body mass and ground reaction forces. At midstance, when ground reaction forces (GRFs) are typically highest and approximately vertical, bending stress/strain at midshaft (the likely location of maximum bending) is a function of many factors, including the magnitude and orientation of GRF relative to the element and the cross-sectional and the material properties of the bone (Biewener et al., 1983). Distal tapering, therefore, leads not How bones respond dynamically to mechanical loading through changes in shape and structure is poorly understood, particularly with respect to variations between bones. Structurally, cortical bones adapt in vivo to their mechanical environments primarily by modulating two processes, modeling and Haversian remodeling. Modeling, defined here as the addition of new bone, may occur in response to mechanical stimuli by altering bone shape or size through growth. Haversian remodeling is thought to be an adaptation to repair microcracks or prevent microcrack propagation. Here, we examine whether cortical bone in sheep limbs modulates periosteal modeling and Haversian remodeling to optimize strength relative to mass in hind-limb midshafts in response to moderate levels of exercise at different growth stages. Histomorphometry was used to compare rates of periosteal growth and Haversian remodeling in exercised and sedentary treatment groups of juvenile, subadult and young adult sheep. In vivo strain data were also collected for the tibia and metatarsal midshafts of juvenile sheep. The results suggest that limb bones initially optimize responses to loading...

SUMMARY Wolff's law of trajectorial orientation proposes that trabecular struts align with the orientation of dominant compressive loads within a joint. Although widely considered in skeletal biology, Wolff's law has never been experimentally tested while controlling for ontogenetic stage, activity level,and species differences, all factors that may affect trabecular bone growth. Here we report an experimental test of Wolff's law using a within-species design in age-matched subjects experiencing physiologically normal levels of bone strain. Two age-matched groups of juvenile guinea fowl Numida meleagris ran on a treadmill set at either 0° (Level group) or 20° (Incline group), for 10 min per day over a 45-day treatment period. Birds running on the 20° inclined treadmill used more-flexed knees than those in the Level group at midstance (the point of peak ground reaction force). This difference in joint posture enabled us to test the sensitivity of trabecular alignment to altered load orientation in the knee. Using a new radon transform-based method for measuring trabecular orientation, our analysis shows that the fine trabecular bone in the distal femur has a high degree of correspondence between changes in joint angle and trabecular orientation. The sensitivity of this response supports the prediction that trabecular bone adapts dynamically to the orientation of peak compressive forces.